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Journal of Convex Analysis 19 (2012), No. 2, 519--524
Copyright Heldermann Verlag 2012

Confexifying the Counting Function on Rp for Convexifying the Rank Function on Mm,n(R)

Hai Yen Le
Institut de Mathématiques, Université P. Sabatier, 118, route de Narbonne, 31062 Toulouse, France

We calculate the convex hull of the so-called counting function restricted to a ball of Rp, and we then use it, with a result of A. Lewis, to recover the convex hull of the rank function restricted to a ball of Mm,n(R), the space of real (m,n)-matrices.

Keywords: Counting function, convex hull, rank of a matrix.

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